用C语言编程实现构建最小生成树的两种算法，可以动态输入

构建最小生成树的两种算法是 Prim 算法和 Kruskal 算法。下面给出使用 C 语言实现这两种算法的代码示例。

1. Prim 算法实现最小生成树

#include <stdio.h>
#include <limits.h>

#define V 5 // 图的顶点数

int minKey(int key[], bool mstSet[])
{
    int min = INT_MAX, min_index;

    for (int v = 0; v < V; v++)
        if (mstSet[v] == false && key[v] < min)
            min = key[v], min_index = v;

    return min_index;
}

void printMST(int parent[], int graph[V][V])
{
    printf("Edge \tWeight\n");
    for (int i = 1; i < V; i++)
        printf("%d - %d \t%d \n", parent[i], i, graph[i][parent[i]]);
}

void primMST(int graph[V][V])
{
    int parent[V];
    int key[V];
    bool mstSet[V];

    for (int i = 0; i < V; i++)
        key[i] = INT_MAX, mstSet[i] = false;

    key[0] = 0;
    parent[0] = -1;

    for (int count = 0; count < V - 1; count++) {
        int u = minKey(key, mstSet);
        mstSet[u] = true;

        for (int v = 0; v < V; v++)
            if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v])
                parent[v] = u, key[v] = graph[u][v];
    }

    printMST(parent, graph);
}

int main()
{
    int graph[V][V];

    printf("Enter the graph matrix: ");
    for (int i = 0; i < V; i++) {
        for (int j = 0; j < V; j++) {
            scanf("%d", &graph[i][j]);
        }
    }

    primMST(graph);

    return 0;
}

2. Kruskal 算法实现最小生成树

#include <stdio.h>
#include <stdlib.h>

struct Edge {
    int src, dest, weight;
};

struct Graph {
    int V, E;
    struct Edge* edge;
};

struct Graph* createGraph(int V, int E)
{
    struct Graph* graph = (struct Graph*) malloc(sizeof(struct Graph));
    graph->V = V;
    graph->E = E;

    graph->edge = (struct Edge*) malloc(graph->E * sizeof(struct Edge));

    return graph;
}

struct subset {
    int parent;
    int rank;
};

int find(struct subset subsets[], int i)
{
    if (subsets[i].parent != i)
        subsets[i].parent = find(subsets, subsets[i].parent);

    return subsets[i].parent;
}

void Union(struct subset subsets[], int x, int y)
{
    int xroot = find(subsets, x);
    int yroot = find(subsets, y);

    if (subsets[xroot].rank < subsets[yroot].rank)
        subsets[xroot].parent = yroot;
    else if (subsets[xroot].rank > subsets[yroot].rank)
        subsets[yroot].parent = xroot;
    else {
        subsets[yroot].parent = xroot;
        subsets[xroot].rank++;
    }
}

int myComp(const void* a, const void* b)
{
    struct Edge* a1 = (struct Edge*) a;
    struct Edge* b1 = (struct Edge*) b;
    return a1->weight > b1->weight;
}

void kruskalMST(struct Graph* graph)
{
    int V = graph->V;
    struct Edge result[V];
    int e = 0;
    int i = 0;

    qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp);

    struct subset* subsets
        = (struct subset*) malloc(V * sizeof(struct subset));

    for (int v = 0; v < V; ++v) {
        subsets[v].parent = v;
        subsets[v].rank = 0;
    }

    while (e < V - 1 && i < graph->E) {
        struct Edge next_edge = graph->edge[i++];

        int x = find(subsets, next_edge.src);
        int y = find(subsets, next_edge.dest);

        if (x != y) {
            result[e++] = next_edge;
            Union(subsets, x, y);
        }
    }

    printf("Following are the edges in the constructed MST\n");
    for (i = 0; i < e; ++i)
        printf("%d -- %d == %d\n", result[i].src, result[i].dest,
               result[i].weight);
    return;
}

int main()
{
    int V, E;
    printf("Enter the number of vertices and edges: ");
    scanf("%d%d", &V, &E);

    struct Graph* graph = createGraph(V, E);

    printf("Enter the edges with weights:\n");
    for (int i = 0; i < E; i++)
        scanf("%d%d%d", &graph->edge[i].src, &graph->edge[i].dest,
              &graph->edge[i].weight);

    kruskalMST(graph);

    return 0;
}

注意：以上代码示例并未进行输入数据的错误处理，实际使用时需要自行添加。